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<div class="subTitle">org.apache.commons.math3.linear</div>
<h2 title="Class RectangularCholeskyDecomposition" class="title">Class RectangularCholeskyDecomposition</h2>
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<pre>public class <span class="strong">RectangularCholeskyDecomposition</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Calculates the rectangular Cholesky decomposition of a matrix.
 <p>The rectangular Cholesky decomposition of a real symmetric positive
 semidefinite matrix A consists of a rectangular matrix B with the same
 number of rows such that: A is almost equal to BB<sup>T</sup>, depending
 on a user-defined tolerance. In a sense, this is the square root of A.</p>
 <p>The difference with respect to the regular <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html" title="class in org.apache.commons.math3.linear"><code>CholeskyDecomposition</code></a>
 is that rows/columns may be permuted (hence the rectangular shape instead
 of the traditional triangular shape) and there is a threshold to ignore
 small diagonal elements. This is used for example to generate <a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html" title="class in org.apache.commons.math3.random"><code>correlated
 random n-dimensions vectors</code></a> in a p-dimension subspace (p < n).
 In other words, it allows generating random vectors from a covariance
 matrix that is only positive semidefinite, and not positive definite.</p>
 <p>Rectangular Cholesky decomposition is <em>not</em> suited for solving
 linear systems, so it does not provide any <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><code>decomposition solver</code></a>.</p></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>2.0 (changed to concrete class in 3.0)</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>, 
<a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a></dd></dl>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#RectangularCholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)">RectangularCholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</code>
<div class="block">Decompose a symmetric positive semidefinite matrix.</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#RectangularCholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix,%20double)">RectangularCholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                                double&nbsp;small)</code>
<div class="block">Decompose a symmetric positive semidefinite matrix.</div>
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<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRank()">getRank</a></strong>()</code>
<div class="block">Get the rank of the symmetric positive semidefinite matrix.</div>
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<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRootMatrix()">getRootMatrix</a></strong>()</code>
<div class="block">Get the root of the covariance matrix.</div>
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<h4>RectangularCholeskyDecomposition</h4>
<pre>public&nbsp;RectangularCholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)
                                 throws <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></pre>
<div class="block">Decompose a symmetric positive semidefinite matrix.
 <p>
 <b>Note:</b> this constructor follows the linpack method to detect dependent
 columns by proceeding with the Cholesky algorithm until a nonpositive diagonal
 element is encountered.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Symmetric positive semidefinite matrix.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if the matrix is not
 positive semidefinite.</dd><dt><span class="strong">Since:</span></dt>
  <dd>3.1</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://eprints.ma.man.ac.uk/1193/01/covered/MIMS_ep2008_56.pdf">
 Analysis of the Cholesky Decomposition of a Semi-definite Matrix</a></dd></dl>
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<h4>RectangularCholeskyDecomposition</h4>
<pre>public&nbsp;RectangularCholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                                double&nbsp;small)
                                 throws <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></pre>
<div class="block">Decompose a symmetric positive semidefinite matrix.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Symmetric positive semidefinite matrix.</dd><dd><code>small</code> - Diagonal elements threshold under which columns are
 considered to be dependent on previous ones and are discarded.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if the matrix is not
 positive semidefinite.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;getRootMatrix()</pre>
<div class="block">Get the root of the covariance matrix.
 The root is the rectangular matrix <code>B</code> such that
 the covariance matrix is equal to <code>B.B<sup>T</sup></code></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>root of the square matrix</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRank()"><code>getRank()</code></a></dd></dl>
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<pre>public&nbsp;int&nbsp;getRank()</pre>
<div class="block">Get the rank of the symmetric positive semidefinite matrix.
 The r is the number of independent rows in the symmetric positive semidefinite
 matrix, it is also the number of columns of the rectangular
 matrix of the decomposition.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>r of the square matrix.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRootMatrix()"><code>getRootMatrix()</code></a></dd></dl>
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